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- Title
Khovanov homology and exotic surfaces in the 4-ball.
- Authors
Hayden, Kyle; Sundberg, Isaac
- Abstract
We show that the cobordism maps on Khovanov homology can distinguish smooth surfaces in the 4-ball that are exotically knotted (i.e., isotopic through ambient homeomorphisms but not ambient diffeomorphisms). We develop new techniques for distinguishing cobordism maps on Khovanov homology, drawing on knot symmetries and braid factorizations. We also show that Plamenevskaya's transverse invariant in Khovanov homology is preserved by maps induced by positive ascending cobordisms.
- Subjects
HOMEOMORPHISMS; DIFFEOMORPHISMS; FACTORIZATION; MAPS; BRAID group (Knot theory); KNOT theory; SYMMETRY
- Publication
Journal für die Reine und Angewandte Mathematik, 2024, Vol 2024, Issue 809, p217
- ISSN
0075-4102
- Publication type
Article
- DOI
10.1515/crelle-2024-0001